Following standard methods, e.g. [1]}, we start by interpolating a point \(x_{i}\)  inside a single tetrahedron using the vertex positions \(x_{i}^\alpha \)  (\(\alpha =1,2,3,4\) ).
The interpolation uses an inscribed, dimensionless coordinate system, denoted by \(\left(\xi _1,\xi _2,\xi _3\right)\)  with \(0\le \xi _i\le 1\)[1]} erroneously states a range of \(-1\le \xi _i\le 1\)  for the tetrahedral element., as depicted in figure REF a.
One vertex defines the origin while the remaining three indicate the coordinate axes.
A set of shape functions, i. e., interpolation functions, \(N^{\alpha }\left(\xi _1,\xi _2,\xi _3\right)\)  is employed to interpolate positions inside the tetrahedron volume.
An arbitrary point \(x_{i}\)  inside the element is interpolated as
\(x_{i} = \sum \limits _{\alpha =1}^{4} N^{\alpha }\left(\xi _1,\xi _2,\xi _3\right)x_{i}^\alpha \:,\) 
